Physical Chemistry , 1st ed.

unhindered in their rotational and vibrational motions, and so both occur si-
multaneously. In the liquid phase, vibrational motions occur relatively unhin-
dered but rotational motions may be hindered. In the solid phase, vibrations
are relatively hindered, and with a few exceptions the rotations are quenched.
A gas-phase sample undergoes vibrational and rotational motion. Vibrations
typically absorb in a certain region of the spectrum, the infrared region.Pure
rotational motions absorb energy in the microwave region of the spectrum,
but the energy involved in a rotational state transition is not negligible com-
pared to the vibrational energy. In the process of absorbing vibrational energy,
many molecules can simultaneously undergo a rotational energy transition.
Although the energy difference due to the vibrational state transition is con-
stant (and equals h), the energy difference due to rotational state transitions
depends on the initial rotational quantum number J. Therefore, the combina-
tion—or superposition—of rotational transitions with a vibrational transition
is also a series of absorptions. Such a series of absorptions, relatively regularly
spaced, typifies rotational-vibrational spectroscopy.Sometimes the term rovi-
brational spectroscopyis used.
The spectrum of gaseous HCl is a classic example of rovibrational spec-
troscopy. An example of an HCl spectrum is shown in Figure 14.35. The series
of absorptions is separated into two distinct regions. From 3100 to 2900 cm^1
is the combination rotational-vibrational change in quantum number (v 1,
J 1), and from 2860 to 2600 cm^1 the quantum number changes are
(v 1,J1). For both regions, or branches,the change in the vibra-
tional quantum number is 1, because in absorption spectroscopy the vibra-
tional quantum number increases. Normally, in pure rotational absorption
spectra, the change in the Jquantum number is also 1. But when a molecule
changes vibrational states, there is the possibility that the molecule can go to
the next vibrational level but also simultaneously to a lower valuefor the J
quantum number. Because going to a lower rotational state implies an overall
loss of energy, the (v 1,J1) transitions appear at lower energies

14.17 Rotational-Vibrational Spectroscopy 507

2.0

0.5

3100

Wavenumbers

2600

Absorbance

1.5

2.5

1.0

3000 2900 2800 2700

Figure 14.35 Complete Pand Rbranches of the rovibrational spectrum of HCl gas. The dou-
blet character of each absorption is due to the natural isotopic abundances of^35 Cl and^37 Cl.